The Interplay between Number Theory and Random Matrix Theory

Thời gian: Bắt đầu từ 9h30, thứ Sáu, ngày 8 tháng 5 năm 2026

Địa điểm: Hội trường 301, Nhà A5, Viện Toán học

Tóm tắt báo cáo: This talk explores the remarkable parallels between the distribution of zeros and values of L-functions and of the characteristic polynomials of random matrices from the classical compact groups.

We begin by examining the Riemann zeta function, reviewing how its zeros dictate the  distribution of prime numbers and how its value distribution, specifically its moments, has remained a central challenge in analytic number theory for over a century.

We will discuss the Katz-Sarnak philosophy, which predicts that certain statistics of various families of L-functions align with the corresponding statistics for the classical compact groups.

We examine how the moments of characteristic polynomials in these matrix groups provide precise conjectures and predictions for L-functions, and how problems in number theory have helped drive the development of random matrix theory and vice versa.